It used to be that with Costco's return policy (pretty much lifetime return as long as you have the sales receipt and all the accessories), you could feel safe buying any electronics there. They've changed that recently, and now limit returns to 3 months for any reason, 6 months for defectives. With that said, most problems show up in the first 6 months, and portables often have 90 day warranties. So it's probably still a good bet to buy from costco.
I'd highly recommend Panasonic portables if you can afford one and find a nice sale. They have the longest track record for making high quality portables. If you decide to buy a cheaper unit, the Mintek portables are pretty decent. The first two I bought had problems and were replaced (first a battery charging issue, then a screen issue). But now that I have one that works well, it has performed flawlessly for about 18 months. MDP-1020 is the model I bought at costco with a 10" screen. I think costco still carries them.
If you are going to have 2 kids that want to view programs, definitely consider the dual display model. Generally the viewing angle on the portables is limited, and getting two to watch one screen could lead to complaints. Although with how cheap some of the 7 inch units are, you can probably buy 2 separate players for about the same price as a dual screen player.
With portables, consider getting an extended warranty given the use by kids (at least my experience has been things tend to get slightly, uhm, beat up). J&R Music World sells extended warranties by Repair Master and you can buy the warranty regardless of where you purchase the player. For one repair in the 2-3 year warranty, it will have paid for itself (a 3 year extended warranty for a player under $200 is $19.99). However, since prices on the portables are in the $100 range, it may not be worth it (especially if you don't mind replacing stuff). But if you are spending close to $200, it may be worth the extra $20. . . .